So also AlphaNumeric states a limit process. This is intriguing to me, Severian, what are the infra-red divergences?

 

You don't really need to worry about the infra-red divergences. They are divergences in our results when you take the momentum in the problem to zero (so a particle loop where you are summing over all momentum including zero, or the emission of a really really "soft" gluon etc).

 

But they are really just an artifact of the way we do the calculations (ie. perturbation theory). They cancel in all physical quantities, without the need to do any renormalization (but are a pain in the butt when doing the calculation).

are world is made of the 1-4 dimensions compressinoing and making are world as we know it the dimensional collapse theory...............what made the collapse is still a mystery that i will find!!!!!!!!!!!!

 

life onlty exist in the 1-4 dimensions the other nine are the force which caused the big bang which forced all matter in are dimension because we are a matter universenot an antimatter universe whichis the next dimension>>>>>>>>>>>>>>>>>

That seems to be a pretty good summary. I've yet to see anything decidedly concrete come out of string theory. Perhaps it would be best to say "string theories", since there are so many of them, though at that point they do seem to make some predictions.

I even routinely do calculations in non-integer numbers of dimensions.

what is the picture you paint?

what is an integer dimension,and what is a non-integer dimension?

what is the picture you paint?

what is an integer dimension,and what is a non-integer dimension?

 

A universe with integer dimension would be one that had either 1, 2, 3, 4, 5 or 6 ... and so on dimensions. A universe with no-integer dimension would have a number lying between these, such as 5.9, or 3.2.

How does this come about in your theoretics?

How does this come about in your theoretics?

 

It doesn't really. It is just a mathematical trick. The equations are better behaved in non-integer momenta (essentially because the expressions have things like [math]1/(d-4)[/math] where [math]d[/math] is the number of dimensions). So we do the calculations in [math]d=4-2\epsilon[/math] dimensions and take the limit [math]\epsilon \to 0[/math] at the end.

 

No-one is suggesting that there really are non-integer dimensions. It is just a convenient trick.

Fun stuff. We mathematicians are somewhat shameless. Two and a half points for a mathematical physicist.

Edited December 17, 200817 yr by Norman Albers

The string theory is interesting, if it is true, how do we prove it. How many dimensions are out there.

 

Blue we can concieve these dimensions, or otherwise, they would not exist within our math and imaginations. However, there is no experimental way to test these theories, which is a different matter all together.

Do you have to ask?

 

Almost has to be Beatriz de Carlos

 

Beatriz was chairing one of the sessions at the UK Annual Theory Meeting which I was at last week. I wonder if I met AlphaNumeric there without realizing.

Beatriz taught some of my Masters courses at Sussex. I doubt she remembers me though.

Could "dimensions" be in an unrealized dynamical phase space?

I don't understand your question fully Norman, but degrees of freedoms can indeed be "dimensions" of some "phase space". (I rather think of the coordinates as degrees of freedom as opposed to the dimensions).

 

For example in phase space (configuration + momentum) canonical transformations are not just diffeomorphisms of the "configuration space" but form a larger group which is a subgroup of diffeomorphisms of the whole phase space.

 

If that is what you are thinking of?

Yes! I know what you are saying up to the last paragraph terms and think I see what you are saying. "degrees of freedom" is indeed what I am thinking. What do you mean by "whole phase space"? This sounds optimistic. I do use the term "phase space face place" to refer to the UNIVERSE. I just wrote to Burinskii: Inside BH horizons I ask why is this not saying propagation in the transverse dimensions tangent to the sphere are severely attenuated,

which might be to say "curled up" ?

Edited December 25, 200817 yr by Norman Albers